Logic Puzzles

[alfonz1986]

Ok, so theres two lemmings sitting in a boat in a lake. One of the lemmings manages to resist the urge of jumping out of the boat, but the other lemming isn't so lucky and walks over the edge into the water and drowns  http://www.lemmingsforums.com/Smileys/lemmings/sick.gif" alt=":sick:" title="Sick" class="smiley" /> His carcass sinks straight to the bottom. What will happen to the overall water level of the lake?
Will it

(a) Rise
(b) Fall
(c) Stay the same


Write your answers on a postcard, and give a little reasoning as to why you think its the right answer  http://www.lemmingsforums.com/Smileys/lemmings/cool.gif" alt="8)" title="Cool" class="smiley" />

[Simon]

Hmm, I might answer it as nobody else wants to, despite knowing it beforehand; it's a popular physics puzzle.

Answer is that the level falls (or stays the same in a corner case). The reasoning is as follows. If he's in the boat, his weight displaces water (putting this water above the regular level) equal to his weight (pressure), whereas if he's in the lake, he displaces water equal to his volume. The water amount equalling his weight is more than his volume; if it were not, he wouldn't have drowned, but floated.

The corner case happens with exact same densities, in which case inertia from falling would have made him drown.

-- Simon

[alfonz1986]

I'm not sure what u mean by the 'corner case'

[chaos_defrost]

I'm not sure what u mean by the 'corner case'

I think he means when the density is the same as water -- the lemming then sinks because he has downwards force from gravity.

[alfonz1986]

Thats not the case, if the lemmings density was equal to the waters, the lemming would be 'neutrally buoyant' and would neither sink or float. Remember gravity is acting on the lemmings and the water.

[finlay]

But he's just either walked or jumped into the lake, and that force isn't gonna go nowhere, so he'll continue falling through the same-density water until he receives a different force from somewhere.

[ccexplore]

Finlay and Simon is right I think.  Neutrally buoyant just means the force of gravity cancels the force of buoyancy, but to stop the falling you still need a net upward force to slow down the downward velocity you've already gained from gravity alone before you hit the water.  As Simon said, this is inertia from falling.

So unless the lemming is so careful in entering the water that he has no downward velocity when he hits the water, he will continue going downwards until he is able to have an upward force exerted on himself to change his velocity from down to up.  For example, once he hits the bottom he could push against the floor to create an upward force on himself, and then he would be able to get back up on the surface.  But if he's a true lemming he would not know to do anything http://www.lemmingsforums.com/Smileys/lemmings/winktounge.gif" alt=";P" title="Wink-Tongue" class="smiley" />, and therefore would've stayed under water.

[edit: I might've simplified the situation a bit when the lemming hits the bottom.  Depending on the material characteristics of the floor, the impact force can be such that I suppose the lemming can also bounce back up, like a billiard ball bouncing off a wall.]

[alfonz1986]

@finlay and ccexplore, the force is dissipated quickly by drag force. The water effectively acts like damping system (suspension system in a car) and slows his velocity to a standstill (assuming he was neutrally buoyant). If he is denser than the water (like in the problem) then he continues sinking due to his downward weight being greater than the upward buoyancy force. His entry velocity from falling in off the boat has nothing to do with it unless the lake was very shallow.

[ccexplore]

@finlay and ccexplore, the force is dissipated quickly by drag force. The water effectively acts like damping system (suspension system in a car) and slows his velocity to a standstill (assuming he was neutrally buoyant).

Okay that's reasonable, but ultimately it still depends on how fast the lemming is when he hits water.  In other words, if the lemming jumped off a 10-floor building he's probably fast enough that even the drag force would not have prevented him from being fully submerged.  Your problem did state that he sinks all the way to the bottom, so for the corner case to occur, it does imply an unrealistic situation (in terms of falling off from a boat) where the lemming hit the water so fast, and the lake shallow enough, that the lemming is still able to hit the bottom despite the drag force.  Still, given that these aspects of the problem is unspecified, it is fair for Simon to posit a corner case to cover this situation as well.

[edit: Hmm......due to the way you posit the problem, technically it can also describe a situation where the lemming first drowns by being fully submerged in water (w/o hitting bottom due to neutral buoyancy and drag), then having swallowed water, the increased density puts him out of neutral buoyancy and then he finally sinks to bottom.  Not sure how the water level works out in that case, although the among of water swallowed should be negligible, since even one molecule of it is enough to put the density past neutral buoyancy.]

[alfonz1986]

We're going off topic a bit here. The problem asks about the water depth, not whether or not the lemming ultimately sinks or floats. Also if the lemming enters the water with more velocity the normal force (drag force) just increases to counteract it. Haven't you heard of firing bullets into water? They completely disintegrate into shrapnel and do not travel far due to the massive drag force counteracting their large velocity. So the question remains ccexplore:

Will the water level rise, fall, or stay the same? and why?

EDIT: for the puposes of the problem, assume that the lemming doesnt swallow any water, or release any air. I only specified the problem with two lemmings in a boat to relate it to all u guys http://www.lemmingsforums.com/Smileys/lemmings/smiley.gif" alt=":)" title="Smiley" class="smiley" /> the real problem was two people in a boat and someone drops a solid object off the boat. although, the basic logic remains the same.

[ccexplore]

We're going off topic a bit here. The problem asks about the water depth, not whether or not the lemming ultimately sinks or floats.

I think Simon already answered your question, you're the one who is disputing the corner case scenario he proposed.  At this point it's just hashing out the details of the corner case to get a better understanding of what is to happen or not happen in that case.  If someone else has a different puzzle I'm sure we're happy to look at it.

Also if the lemming enters the water with more velocity the normal force (drag force) just increases to counteract it. Haven't you heard of firing bullets into water? They completely disintegrate into shrapnel and do not travel far due to the massive drag force counteracting their large velocity.

They've actually done a http://en.wikipedia.org/wiki/MythBusters_(2005_season)#Episode_34_.E2.80.93_.22Bulletproof_Water.22" class="bbc_link" target="_blank">TV show related to bullets firing into water.  There's no question that you get higher drag force with higher velocity, but not knowing the exact numbers, it doesn't directly answer the question of how much distance it takes to reach 0 velocity with drag.  For example the TV show found that slower-speed bullets can travel for at least 8 feet in water.  I'll grant you that water exerts far higher drag than air, so I don't disagree with what you suggest will happen even if I'm not certain either.

I think this calls for an experiment.  Who has a lemming we can drown? http://www.lemmingsforums.com/Smileys/lemmings/winktounge.gif" alt=";P" title="Wink-Tongue" class="smiley" />

=========

Aside: the highly physical nature of the problem makes me think it's not really a logic puzzle to start with.  So we already started a bit off-topic.

[Simon]

http://blogs.1077theend.com/files/2010/07/Beavis_and_Butthead_horror.png" alt="" class="bbc_img" />

Physics sucks!

Beavis has 23 fleas in his hair, and 32 spiders. Butt-head thinks this sucks too, and decides to remove the critters with a fork. The fork will always pick 2 critters at once.

If at least one of the two is a spider, he flings it out the window and puts the other critter (either flea or spider) back into the hair. If both are fleas, he carefully takes them to the trash bin outside. While Butt-head is underway, Beavis gets bored, searches the living room walls for a fresh spider, and puts that in his hair.

Butt-head continues this, until eventually, only a single critter is left in the hair. What species is it?

-- Simon

[alfonz1986]

The answer is a Flea. He has an odd number of fleas and no way of getting rid of the final flea since the only way he can discard fleas is two at a time.

[edit - added] That being said, the final combinations are:

FSS - FS > FS > F
or
FSS - SS > FS > F

FFF - FF > F

even if he adds the spider right at the end it would give FS > F

[Simon]

Yep, it's perfect. The important observations are that each iteration lowers the critters remaining by 1, and that the fleas may only go in pairs.

Post another one or declare open floor. :-)

-- Simon

[alfonz1986]

hehe, but u already knew the answer to my puzzle. did u manage to get it urself first go?

if u know the answer to this next one already - let the others ponder it a bit longer http://www.lemmingsforums.com/Smileys/lemmings/smiley.gif" alt=":)" title="Smiley" class="smiley" />

Ok here it is:

Theres an airplane on a giant conveyor belt on a runway. As the airplane speeds up, the conveyor belt matches the airplane's speed but in the opposite direction. Will the plane be able to takeoff or not? and why?